larfb(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

🎀 NAME 🎀

larfb(3) — straight from the Library Functions Manual — is all about larfb: apply block Householder reflector. Bestie, it’s giving block-reflector main character energy. 💅✨

✨ SYNOPSIS ✨

🧚 Functions

🌸 clarfb 🌸

       subroutine clarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt,
           c, ldc, work, ldwork)

CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

🦋 dlarfb 🦋

       subroutine dlarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt,
           c, ldc, work, ldwork)

DLARFB applies a block reflector or its transpose to a general rectangular matrix.

🎀 slarfb 🎀

       subroutine slarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt,
           c, ldc, work, ldwork)

SLARFB applies a block reflector or its transpose to a general rectangular matrix.

💜 zlarfb 💜

       subroutine zlarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt,
           c, ldc, work, ldwork)

ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

🌈 Detailed Description 🌈

Okay so this is the detailed part, and the function docs are right below. Buckle up, bestie — there’s a lot of literal parameter tea here. 🍓

💖 Function Documentation 💖

🌸 subroutine clarfb 🌸

   subroutine clarfb (character side, character trans, character direct,
       character storev, integer m, integer n, integer k, complex, dimension(
       ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt,
       complex, dimension( ldc, * ) c, integer ldc, complex, dimension( ldwork,
       * ) work, integer ldwork)

CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

✨ Purpose

CLARFB applies a complex block reflector H or its transpose H**H to a complex M-by-N matrix C, from either the left or the right. 💖

🌸 Parameters

  • SIDE — CHARACTER*1. 'L' means apply H or H**H from the Left; 'R' means apply H or H**H from the Right. 🫶
  • TRANS — CHARACTER*1. 'N' means apply H (No transpose); 'C' means apply H**H (Conjugate transpose). 💅
  • DIRECT — CHARACTER*1. This tells you how H is formed from a product of elementary reflectors: 'F' gives H = H(1) H(2) . . . H(k) (Forward); 'B' gives H = H(k) . . . H(2) H(1) (Backward). ✨
  • STOREV — CHARACTER*1. This tells you how the vectors which define the elementary reflectors are stored: 'C' means Columnwise; 'R' means Rowwise. 🦋
  • M — INTEGER. The number of rows of the matrix C. 📏
  • N — INTEGER. The number of columns of the matrix C. 📐
  • K — INTEGER. The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector). If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. 👑
  • V — COMPLEX array, dimension (LDV,K) if STOREV = 'C'; (LDV,M) if STOREV = 'R' and SIDE = 'L'; (LDV,N) if STOREV = 'R' and SIDE = 'R'. The matrix V. See Further Details. 🌟
  • LDV — INTEGER. The leading dimension of the array V. If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); if STOREV = 'R', LDV >= K. 🎯
  • T — COMPLEX array, dimension (LDT,K). The triangular K-by-K matrix T in the representation of the block reflector. 🔥
  • LDT — INTEGER. The leading dimension of the array T. LDT >= K. 🧚
  • C — COMPLEX array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H. 😭
  • LDC — INTEGER. The leading dimension of the array C. LDC >= max(1,M). 💀
  • WORK — COMPLEX array, dimension (LDWORK,K). 🍓
  • LDWORK — INTEGER. The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= max(1,N); if SIDE = 'R', LDWORK >= max(1,M). 🌈

👑 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🔥 Further Details

The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. The triangular part of V (including its diagonal) is not referenced. 💖

  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':

               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
                   ( v1  1    )                     (     1 v2 v2 v2 )
                   ( v1 v2  1 )                     (        1 v3 v3 )
                   ( v1 v2 v3 )
                   ( v1 v2 v3 )

  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':

               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
                   (     1 v3 )
                   (        1 )

Definition at line 194 of file clarfb.f. 🎀

🔥 subroutine dlarfb 🔥

   subroutine dlarfb (character side, character trans, character direct,
       character storev, integer m, integer n, integer k, double precision,
       dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, *
       ) t, integer ldt, double precision, dimension( ldc, * ) c, integer ldc,
       double precision, dimension( ldwork, * ) work, integer ldwork)

DLARFB applies a block reflector or its transpose to a general rectangular matrix.

✨ Purpose

DLARFB applies a real block reflector H or its transpose H**T to a real m by n matrix C, from either the left or the right. 💜

🦋 Parameters

  • SIDE — CHARACTER*1. 'L' means apply H or H**T from the Left; 'R' means apply H or H**T from the Right. 🫶
  • TRANS — CHARACTER*1. 'N' means apply H (No transpose); 'T' means apply H**T (Transpose). 💅
  • DIRECT — CHARACTER*1. This tells you how H is formed from a product of elementary reflectors: 'F' gives H = H(1) H(2) . . . H(k) (Forward); 'B' gives H = H(k) . . . H(2) H(1) (Backward). ✨
  • STOREV — CHARACTER*1. This tells you how the vectors which define the elementary reflectors are stored: 'C' means Columnwise; 'R' means Rowwise. 🦋
  • M — INTEGER. The number of rows of the matrix C. 📏
  • N — INTEGER. The number of columns of the matrix C. 📐
  • K — INTEGER. The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector). If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. 👑
  • V — DOUBLE PRECISION array, dimension (LDV,K) if STOREV = 'C'; (LDV,M) if STOREV = 'R' and SIDE = 'L'; (LDV,N) if STOREV = 'R' and SIDE = 'R'. The matrix V. See Further Details. 🌟
  • LDV — INTEGER. The leading dimension of the array V. If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); if STOREV = 'R', LDV >= K. 🎯
  • T — DOUBLE PRECISION array, dimension (LDT,K). The triangular k by k matrix T in the representation of the block reflector. 🔥
  • LDT — INTEGER. The leading dimension of the array T. LDT >= K. 🧚
  • C — DOUBLE PRECISION array, dimension (LDC,N). On entry, the m by n matrix C. On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. 😭
  • LDC — INTEGER. The leading dimension of the array C. LDC >= max(1,M). 💀
  • WORK — DOUBLE PRECISION array, dimension (LDWORK,K). 🍓
  • LDWORK — INTEGER. The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= max(1,N); if SIDE = 'R', LDWORK >= max(1,M). 🌈

👑 Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🔥 Further Details

okay so here’s the visual, bestie — the shape of V and how the vectors that define the H(i) are stored is literally best illustrated by this example with n = 5 and k = 3. The triangular part of V (diagonal included) is not referenced, so don’t come for it 💅

DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':

             V = (  1       )                 V = (  1 v1 v1 v1 v1 )
                 ( v1  1    )                     (     1 v2 v2 v2 )
                 ( v1 v2  1 )                     (        1 v3 v3 )
                 ( v1 v2 v3 )
                 ( v1 v2 v3 )

DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':

             V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
                 ( v1 v2 v3 )                     ( v2 v2 v2  1    )
                 (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
                 (     1 v3 )
                 (        1 )
Definition at line 194 of file dlarfb.f.

💖 subroutine slarfb

subroutine slarfb (character side, character trans, character direct,
    character storev, integer m, integer n, integer k, real, dimension( ldv,
    * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real,
    dimension( ldc, * ) c, integer ldc, real, dimension( ldwork, * ) work,
    integer ldwork)

SLARFB applies a block reflector or its transpose to a general rectangular matrix. Real ones only, bestie — this is the REAL girlie 💅

✨ Purpose

SLARFB applies a real block reflector H or its transpose H**T to a real m by n matrix C, from either the left or the right.

🫶 Parameters

  • SIDE — SIDE is CHARACTER*1. = 'L': apply H or H**T from the Left. = 'R': apply H or H**T from the Right.
  • TRANS — TRANS is CHARACTER*1. = 'N': apply H (No transpose). = 'T': apply H**T (Transpose).
  • DIRECT — DIRECT is CHARACTER*1. Tells you how H is formed from a product of elementary reflectors. = 'F': H = H(1) H(2) . . . H(k) (Forward). = 'B': H = H(k) . . . H(2) H(1) (Backward).
  • STOREV — STOREV is CHARACTER*1. Tells you how the vectors which define the elementary reflectors are stored. = 'C': Columnwise. = 'R': Rowwise.
  • M — M is INTEGER. The number of rows of the matrix C.
  • N — N is INTEGER. The number of columns of the matrix C.
  • K — K is INTEGER. The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector). If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
  • V — V is REAL array, dimension (LDV,K) if STOREV = 'C'; (LDV,M) if STOREV = 'R' and SIDE = 'L'; (LDV,N) if STOREV = 'R' and SIDE = 'R'. The matrix V. See Further Details.
  • LDV — LDV is INTEGER. The leading dimension of the array V. If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
  • T — T is REAL array, dimension (LDT,K). The triangular k by k matrix T in the representation of the block reflector.
  • LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= K.
  • C — C is REAL array, dimension (LDC,N). On entry, the m by n matrix C. On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
  • LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
  • WORK — WORK is REAL array, dimension (LDWORK,K).
  • LDWORK — LDWORK is INTEGER. The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= max(1,N); if SIDE = 'R', LDWORK >= max(1,M).

💌 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🦋 Further Details

The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. The triangular part of V (including its diagonal) is not referenced.

DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':

             V = (  1       )                 V = (  1 v1 v1 v1 v1 )
                 ( v1  1    )                     (     1 v2 v2 v2 )
                 ( v1 v2  1 )                     (        1 v3 v3 )
                 ( v1 v2 v3 )
                 ( v1 v2 v3 )

DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':

             V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
                 ( v1 v2 v3 )                     ( v2 v2 v2  1    )
                 (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
                 (     1 v3 )
                 (        1 )
Definition at line 194 of file slarfb.f.

🌈 subroutine zlarfb

subroutine zlarfb (character side, character trans, character direct,
    character storev, integer m, integer n, integer k, complex*16,
    dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t,
    integer ldt, complex*16, dimension( ldc, * ) c, integer ldc, complex*16,
    dimension( ldwork, * ) work, integer ldwork)

ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. And yes, she’s COMPLEX*16 — we’re in our complex era 🔥

✨ Purpose

ZLARFB applies a complex block reflector H or its transpose H**H to a complex M-by-N matrix C, from either the left or the right.

🫶 Parameters

  • SIDE — SIDE is CHARACTER*1. = 'L': apply H or H**H from the Left. = 'R': apply H or H**H from the Right.
  • TRANS — TRANS is CHARACTER*1. = 'N': apply H (No transpose). = 'C': apply H**H (Conjugate transpose).
  • DIRECT — DIRECT is CHARACTER*1. Indicates how H is formed from a product of elementary reflectors. = 'F': H = H(1) H(2) . . . H(k) (Forward). = 'B': H = H(k) . . . H(2) H(1) (Backward).
  • STOREV — STOREV is CHARACTER*1. Indicates how the vectors which define the elementary reflectors are stored. = 'C': Columnwise. = 'R': Rowwise.
  • M — M is INTEGER. The number of rows of the matrix C.
  • N — N is INTEGER. The number of columns of the matrix C.
  • K — K is INTEGER. The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector). If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
  • V — V is COMPLEX*16 array, dimension (LDV,K) if STOREV = 'C'; (LDV,M) if STOREV = 'R' and SIDE = 'L'; (LDV,N) if STOREV = 'R' and SIDE = 'R'. See Further Details.
  • LDV — LDV is INTEGER. The leading dimension of the array V. If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
  • T — T is COMPLEX*16 array, dimension (LDT,K). The triangular K-by-K matrix T in the representation of the block reflector.
  • LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= K.
  • C — C is COMPLEX*16 array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
  • LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
  • WORK — WORK is COMPLEX*16 array, dimension (LDWORK,K).
  • LDWORK — LDWORK is INTEGER. The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= max(1,N); if SIDE = 'R', LDWORK >= max(1,M).

💌 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🌸 Further Details

okay so bestie, the shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by this example with n = 5 and k = 3. and lowkey important: the triangular part of V (including its diagonal) is not referenced — don't @ me, that's just how it is 💅

           !>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
           !>
           !>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
           !>                   ( v1  1    )                     (     1 v2 v2 v2 )
           !>                   ( v1 v2  1 )                     (        1 v3 v3 )
           !>                   ( v1 v2 v3 )
           !>                   ( v1 v2 v3 )
           !>
           !>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
           !>
           !>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
           !>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
           !>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
           !>                   (     1 v3 )
           !>                   (        1 )
           !>

📍 oh and btw, the definition is at line 194 of file zlarfb.f — slay.

👑 AUTHOR 👑

this whole page was generated automatically by Doxygen for LAPACK from the source code. no cap, the robots did it 💅✨

anyway bestie, that's the whole page! it's from LAPACK Version 3.12.0, and the page is larfb(3) — stay iconic 💖🦋🌸

📦 where this page comes from